Communicating with light – fibre optics

Activity 2

Illustrating the inverse square law of radiation

There are some major problems with using light to send messages over a long distance. One of these is because light gradually becomes weaker as it radiates out from a source.

In this activity you will determine how illumination varies with the distance from the light source.

Materials (for the class)

  • electric light with a 60-watt bulb
  • camera with a built-in light meter
  • sheet of greaseproof paper (approximately 10 × 10 centimetres)
  • sticky tape

Materials (for each person)

  • a sheet of log-log graph paper

Procedure

  1. Prepare a table with headings as follows:
    Distance between camera and light source Exposure time
  2. Attach the piece of greaseproof paper so that it covers the lens of the camera. (Do not put any tape on the camera lens.)
  3. Darken the room.
  4. Place the light source at one end of the darkened room.
  5. Get as far away as possible from the light (5-10 metres).
  6. Set the camera shutter on the slowest speed (1 second).
  7. Point the camera at the light. Adjust the lens aperture setting so that the pointer on the exposure meter comes to a clearly defined mark (the 'correct' exposure) on its scale.
  8. Measure the distance between the light source and the camera.
  9. Record on your table the distance and the exposure time.
  10. Move the camera closer to the light, by about one-third of the distance, and measure that distance. (For example, if the initial distance was 9 metres, move the camera to 6 metres.)
  11. Point the camera at the light. Leave the lens aperture setting unchanged and change the shutter speed until the pointer returns to the same position that it was on in step 7.
  12. Record on your table the distance and the exposure time.
  13. Repeat steps 10, 11, and 12 until you get to the shortest exposure time allowed by the camera (1/1000 second). (The subsequent distances for the example given in step 10 would be 4 metres, 2.7 metres, 1.8 metres, 1.2 metres, 0.8 metres, 0.5 metres, and 0.33 metres.)
  14. Plot your exposure setting against distance on log-log graph paper.
  15. Draw a line of best fit and calculate the slope of the line.

Questions

  1. What is the slope of your line?
  2. Illumination is proportional to the reciprocal of the exposure setting. What does the slope of your line tell you about the relationship between distance and illumination?

Teachers notes

  1. The graphed line should have a slope of +2.
  2. Since illumination is proportional to the reciprocal of the exposure setting, students should see an inverse square relation.

The equation to describe the behaviour of light is the inverse square law of radiation:

E = I/D2

where E is the illumination, I is the luminous intensity of the light source, and D is the distance between the source and the point or object.

Because the energy from a point source spreads out equally in all directions, the illumination it produces diminishes as the inverse square of the distance.

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Posted May 1997.